A steel ball of radius 2.0 mm and density 7800 kg/m³ is dropped into a tall jar of glycerol…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A steel ball of radius and density is dropped into a tall jar of glycerol. The glycerol has a density of and a viscosity of . Find the steady speed of the ball, and check that Stokes' law applies by calculating the Reynolds number. Then find the time that the ball takes to fall at this speed, ignoring the start.
Need a reminder? The key ideaShow
Poiseuille: . Stokes: a steady speed , valid when is below about . Ostwald viscometer: . For a liquid, , which falls as rises.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , , , .
Step 1. The steady speed. We use Stokes' law with the radius in metres, and .
Step 2. The Reynolds number. . This is below , so Stokes' law is a good model.
Step 3. The time. .
Check. The speed is small because glycerol is very viscous. In a thin liquid such as water the same ball would fall much faster, the Reynolds number would be large, and Stokes' law would not hold.
Answer: , and .
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